 2.4 Complexity. Assume \((R,\mathfrak {m})\)  is local and \(M,N\in \operatorname{mod}(R)\) . Then the complexity of the pair \((M,N)\) , defined by Avramov and Buchweitz [1]}, is:
\(\operatorname{cx}_R(M,N)=\inf \lbrace  b\in \mathbb {N}\mid \exists a\in \mathbb {R}\text{ such that } \nu _R(\operatorname{Ext}^n_R(M,N))\le a n^{b-1} \text{ for all } n\gg 0\rbrace ,\) 
